The earliest low-flow frequency study by the USGS in Georgia was completed by Thomson and Carter (1963), who assessed the impacts of the 1954 drought on streamflow and described graphical regression methods for estimating low-flow frequency statistics. Carter (1977) developed low-flow profiles for the upper stem of the Flint River Basin (Apalachicola subregion, fig. 2) by using streamflow data from seven CR streamgages and miscellaneous base-flow measurements made at various locations along the river. Carter and Putnam (1978) presented annual low-flow frequency statistics for 134 CR streamgages and 102 partial-record (PR) stations in Georgia. PR stations are sites that only have miscellaneous streamflow measurements and are not CR streamgages; many times, PR stations are measured only during low-flow conditions. Carter and Fanning (1982) presented monthly low-flow frequency statistics for 129 selected streamgages in Georgia. Carter (1983) assessed the effects of the 1980–81 drought on streamflow in Georgia. Carter and others (1986; 1988a, b, c, d; 1989a, b) developed 7Q10-flow profiles for selected streams in Georgia. These 7Q10-flow profiles incorporated low-flow data from previous USGS reports. Stamey (1996) presented low-flow characteristics for 12 selected streamgages in southwestern Georgia, southeastern Alabama, and northwestern Florida, which were updated in 2010 (Stamey, 2011). Stamey (2001) presented low-flow characteristics for four selected streamgages located in the Fort Gordon military base in Georgia. Gotvald (2016) presented annual and monthly 1Q10 and 7Q10 statistics for 197 CR streamgages in Georgia that had a minimum of 10 years of record. The study included 85 streamgages on unregulated streams with minimal upstream diversions, 69 streamgages that were known, or considered, to be affected by varying degrees of upstream diversions, and 43 streamgages on regulated streams. Using statistics from 56 streamgages in northern Georgia along with streamgages from Alabama, Tennessee, North Carolina, and South Carolina that were within 75 miles of the State’s borders, Gotvald (2017) used weighted left-censored regression techniques to develop regional regression equations for annual 1Q10 and 7Q10, monthly 7Q10, and mean annual flow that can be used to predict these statistics at ungaged locations in north Georgia located above the Fall Line—the geographic boundary separating the higher elevations of the Southwestern Appalachians, Ridge and Valley, Blue Ridge, and Piedmont ecoregions from the low-lying Southeastern Plains, Middle Atlantic Coastal Plain, and Southern Coastal Plain ecoregions (Cooke, 1936; fig. 1).

Prior to World War II, low-flow characteristics of North Carolina streams had been determined only for CR streamgages. The economic expansion that followed World War II caused an increasing need for hydrologic information at sites where no data had previously been collected (Yonts, 1971). Thus, the USGS expanded its data-collection program in the late-1940s to include PR stations where streamflow measurements were made on a periodic basis. Discharge measurements made under base-flow conditions, along with observations of zero flow, provided the data used in the initial assessments of low-flow characteristics of streams in North Carolina. With data available from the network of PR stations, the USGS began to respond to requests for low-flow characteristics on a site-specific basis, including for ungaged sites.

Several low-flow studies were completed in the 1960s and 1970s in North Carolina. Goddard (1963) presented low-flow characteristics for many CR streamgages in North Carolina, along with drainage area and 7Q10 discharge profiles developed for selected main-stem rivers. Yonts (1971) reported base-flow measurements made at more than 2,200 locations, including CR streamgages and PR stations throughout the State.

Giese and Mason (1993) evaluated low-flow characteristics at 122 CR streamgages and 396 PR stations having drainage areas ranging from 1 to 400 square miles (mi²) and streamflow unaffected by regulation or diversions. Sites were characterized based on similarity in range of low flow and potential to sustain base flow. Ten hydrologic areas (HAs) were delineated in North Carolina, and regression equations relating low-flow characteristics to basin characteristics were developed for ungaged sites. Equations for 4 of the 10 hydrologic areas—HA10, representing the mountains and western Piedmont; HA3, representing the Sand Hills; HA5, representing the eastern Piedmont; and HA9, representing the central Piedmont—had standard errors considered small enough to permit use of regression equations to predict low-flow characteristics at ungaged sites.

Evett (1994) investigated effects of urbanization and land-use changes on low flows. Trends of decreasing low flows with increasing urbanization were detected in data from selected CR streamgages in the Asheville, Charlotte, Greensboro, and Raleigh metropolitan areas and from streamgages in nearby rural areas. Because of the downward trends noted at both urban and rural streamgages used in the analysis, Evett described the results as statistically inconclusive.

During 1996–2003, five reports about basin-wide low-flow investigations were published (Weaver, 1996, 1997, 1998; Weaver and Pope, 2001; Weaver and Fine, 2003) as part of the former North Carolina Division of Water Quality program of assessment and management of water quality in major river basins of North Carolina. These reports summarize low-flow characteristics of streamgages in the basins and present stream profiles of low-flow statistics and drainage areas for selected streams. The stream profiles are graphs of selected low-flow characteristics or drainage area (vertical axis) versus the stream’s river mile (horizontal axis). These graphs provide a visual depiction of changes in at-site low-flow statistics and drainage area along the river length being analyzed, with contributions from major tributaries indicated. The stream profiles include the 7Q10, 30Q2, W7Q10, and 7Q2 low-flow statistics.

The Roanoke River Basin (Chowan-Roanoke subregion, fig. 2) low-flow investigation included 82 streamgages (79 sites in North Carolina and 3 sites in Virginia) and 10 stream profiles (Weaver, 1996). Drainage areas for profiled streams range from 22 mi² to about 9,700 mi².

The Deep River Basin (Cape Fear subregion, fig. 2) low-flow investigation included 7 CR streamgages, 23 PR stations, and stream profiles for the Deep River (Weaver, 1997). The Deep River Basin, in the central Piedmont Physiographic Province of North Carolina, drains slightly more than 1,440 mi² in parts of Chatham, Guilford, Moore, and Randolph Counties. The Deep River is a tributary to the Cape Fear River.

The Neuse River Basin (Neuse-Pamlico subregion, fig. 2) low-flow investigation included 50 CR streamgages, 113 PR stations, and 10 stream profiles (Weaver, 1998). Drainage areas for the profiled streams range from 9 to about 5,600 mi².

The Cape Fear River Basin (Cape Fear subregion, fig. 2) low-flow investigation included 67 CR streamgages, 121 PR stations, and 13 stream profiles (Weaver and Pope, 2001). Drainage areas for the profiled streams range from about 44 to almost 9,100 mi². Because the Deep River is part of the Cape Fear River Basin, the summary of low-flow characteristics at CR streamgages and PR stations in the Deep River Basin (Weaver, 1997) was republished in the Cape Fear River report (Weaver and Pope, 2001) but did not include the Deep River profiles or associated discussions of low-flow characteristics.

The Rocky River Basin (Pee Dee subregion, fig. 2) low-flow investigation included 12 CR streamgages, 44 PR stations, and stream profiles for Rocky River (Weaver and Fine, 2003). The Rocky River Basin, in the southern Piedmont Physiographic Province of North Carolina, drains slightly more than 1,410 mi² in parts of Anson, Cabarrus, Iredell, Mecklenburg, Rowan, Stanly, and Union Counties. The Rocky River is tributary to the Pee Dee River.

By using streamflow data through water year 2012, Weaver (2015) presented updated low-flow frequency and daily flow-duration statistics for 177 unregulated sites, 56 regulated sites, and 33 sites known or considered to be affected by varying degrees of minor regulation and (or) diversions upstream of streamgages. Low-flow frequency statistics included in the report were the 7Q10, W7Q10, 30Q2, and 7Q2 streamflow. At 63 unregulated streamgages in North Carolina that had at least 30 years of record as of CY 1998, the updated 7Q10 statistics were compared with previously computed values.

In addition to the previously referenced USGS reports about low-flow investigations for North Carolina streams, the USGS had traditionally provided a service of estimating low-flow statistics for ungaged locations in North Carolina in response to site-specific requests since the 1950s. With the release of updated techniques in 2026 for estimating low-flow statistics, as documented in this report and implemented within the USGS StreamStats application (USGS, 2019), users will be able to use StreamStats for estimating unregulated low-flow statistics at ungaged locations on streams in Georgia, North Carolina, and South Carolina. Because most requests for low-flow statistics have been for ungaged locations on streams known or considered to be unaffected by regulation and (or) major diversions, StreamStats application will be a suitable replacement for this service.

Stallings (1968) presented low-flow statistics for 61 CR streamgages and 83 PR stations where flow was measured during the 1954 drought (Thomson and Carter, 1963; Stallings, 1968). Johnson and others (1968) focused on low-flow statistics of streams in Pickens County. Streamflow measurements during low-flow conditions from 1945 through 1967 were presented for 32 PR stations. The PR stations were correlated with one of four potential index streamgages, which are CR streamgages suitable for correlation with selected PR stations, to estimate 7Q2 and 7Q10 streamflows.

Bloxham and others (1970) presented magnitude and frequency of low flows for nine CR streamgages in Spartanburg County (Edisto-Santee subregion, fig. 2), and streamflow measurements were presented for 63 sites. At 35 of the 63 sites, correlation techniques were used with index streamgages to estimate their 7Q2 and 7Q10. Bloxham (1976) used data from six index streamgages from the Inner (also referred to as Upper) Coastal Plain (defined as the portion of the Coastal Plain Physiographic Province [Fenneman, 1946] where elevations are about 200 feet [ft] or more above mean sea level [Bloxham, 1976]; fig. 2) to estimate the 7Q2 and 7Q10 at 54 PR stations. Bloxham (1979) used data through CY 1976 to compute low-flow frequency and flow-duration estimates at 71 CR streamgages in South Carolina.

Bloxham (1981) estimated the 7Q2 and 7Q10 at 113 PR stations in the Piedmont and lower (where elevations are below about 200 ft above mean sea level) Coastal Plain Physiographic Provinces of South Carolina (fig. 2). Barker (1986) described 361 PR stations and provided measurements that were made from August 1980 through July 1986. Zalants (1991a) provided estimates of the 7Q2 and 7Q10 at 564 PR stations and 27 CR streamgages on streams in the Blue Ridge and Piedmont Physiographic Provinces, and the Upper Coastal Plain in South Carolina and parts of North Carolina and Georgia. Zalants (1991b; fig. 2) provided estimates of annual minimum 1-, 3-, 7-, 14-, 30-, 60-, and 90-day average streamflow with recurrence intervals of 2 to 50 years (depending on length of record), for 55 CR streamgages in South Carolina when at least 5 years of unregulated daily mean streamflow data were available through CY 1986.

Feaster and Guimaraes (2009, 2012, 2014, and 2016) and Guimaraes and Feaster (2010) presented low-flow statistics in the Pee Dee (Pee Dee subregion, fig. 2); Saluda, Congaree, and Edisto (Edisto-Santee subregion); Catawba-Wateree and Santee (Edisto-Santee subregion); Savannah (Ogeechee-Savannah subregion) and Salkehatchie (Edisto-Santee subregion); and Broad (Edisto-Santee subregion) River Basins in South Carolina for 17, 25, 12, 28, and 24 CR streamgages, respectively. Low-flow estimates for the Pee Dee, Saluda-Congaree-Edisto, Catawba-Wateree and Santee, Savannah and Salkehatchie, and Broad River Basins were computed by using daily mean flow data through CYs 2006, 2008, 2011, 2013, and 2007, respectively. In addition, daily flow durations of the 5- to 95-percent probabilities of exceedance were presented for most of these streamgages. Feaster and Guimaraes (2017) summarized the findings from their five previously published USGS reports and provided a trend analysis for the annual minimum 7-day average flows as well as assessments of long-term annual precipitation. They also assessed the statewide variability in the annual minimum 7-day average flow at eight long-term streamgages.

Streamgages were selected, and low-flow frequency statistics were calculated for streamgages that had a minimum of 10 years of daily mean flows as of March 31, 2022 (end of CY 2021). The mean annual flow and flow-duration statistics were calculated for streamgages that had at least 10 water years of daily mean flow data through September 30, 2021. Streamgages that were considered tidally influenced at low flows were excluded from the study. These criteria resulted in 711 streamgages within the 3-State study area (table 1). For the purposes of regional regression analysis, 132 additional streamgages in Alabama, Florida, Tennessee, and Virginia were analyzed because they share basins with Georgia, North Carolina, and South Carolina or are within about 50 miles of these State boundaries (fig. 1; table 1). These criteria resulted in 843 streamgages for which low-flow frequency, mean annual flow, and flow-duration statistics were computed in this study. However, low-flow frequency and mean annual flow statistics needed for water-resources requirements in Alabama, Florida, Tennessee, and Virginia should be obtained from the most recent USGS streamflow statistics reports for those States. The daily mean flow data for these streamgages are available through web-based retrievals from the National Water Information System (USGS, 2022).

Streamflow data were reviewed for quality control and quality assurance purposes and to assess potential effects from regulation or diversions. Plots of annual minimum n-day average flows and cumulative annual minimum n-day average flows against CY, known as a single-mass curve (Bohman and Patterson, 1993), were reviewed for each streamgage. Consistency in the slope of the single-mass curve indicates a consistency in the streamflow statistic being reviewed through time. Relatively wet or dry periods may cause a short-term change in the slope of the curve, but then the curve reverts to the previous slope when the streamflow regime returns to a more normal condition. However, a curve with a substantial change in the slope that persists and does not revert to the previous slope can indicate a change in the flow regime that could be related to changes in precipitation, land use, or other anthropogenic influences. See sidebar “Example of Single-Mass Curve Analysis” for an example.

Low-flow frequency statistics, as defined in this report, are values of annual minimum daily mean streamflow averaged over designated periods (Riggs, 1972). Note that the use of “average” with respect to the low-flow statistics in this report refers to the arithmetic mean. For example, 7Q10 is one of the most used low-flow statistics and is defined as the annual minimum 7-day average flow with a 10-year recurrence interval. In terms of probability of occurrence, there is a 1 in 10 chance (or 10-percent probability) that the annual minimum 7-day average streamflow in any single year will be equal to or less than the estimated 7Q10 for a specific location (Riggs, 1968, 1972, 1985).

For this study, low-flow frequency statistics were computed by fitting a Pearson Type III distribution to the base 10 logarithms (LPIII) of the annual minimum n-day average streamflow and determining flow estimates for the recurrence intervals of interest (Riggs, 1972). Fitting the distribution required calculating the mean, standard deviation, and skew coefficient of the logarithms of the n-day streamflow. Estimates of the n-day non-exceedance flows for a specified recurrence interval T were computed by using the following equation:Log QT=X¯+KTS,(1)where

Zero flows cannot be included in an LPIII distribution because they cannot be transformed logarithmically. When zero flows are part of the n-day flows at a streamgage, a conditional probability adjustment can be made to estimate the low-flow characteristics (Jennings and Benson, 1969; Tasker, 1987). Additional information on the procedures and guidelines for the conditional probability adjustment can be found in the USGS Surface Water Branch Technical Memorandum No. 70.07 (Carter, 1969).

Active and discontinued USGS streamgages having at least 10 years of record were included in this study. Ten years of record is widely considered as the minimum period of record sufficient for this type of frequency analysis (Riggs, 1972). Frequency statistics were computed for the annual 1Q10, 7Q10, 7Q2, 30Q2, and 30Q3 streamflows; the W7Q10 (November–March) streamflow; and the monthly 1Q10 and 7Q10 streamflows (tables 1 and 2 in Kolb and others, 2026).

Flow-duration curves are cumulative frequency curves that show the percentage of time when specified flows were equaled or exceeded during the period analyzed (Searcy, 1959). Flow durations are computed by sorting the individual daily mean flows for the period of record being analyzed from the largest to the smallest value and assigning each value a rank, starting from 1 to the largest value. The frequencies of exceedance are then computed by using the Weibull formula for computing plotting positions (Helsel and others, 2020):P=100*[M/n+1],(2)where

Streamgages included in the flow-duration analyses have a minimum of 10 years of daily mean flows as of September 30, 2021, which is the end of the water year 2021 (tables 1 and 2 in Kolb and others, 2026).

Trends for the annual minimum 7-day average flows were analyzed for all stations in the investigation by using a probability value (p-value) of 0.05 to determine significance (Kendall, 1938; Helsel and Hirsch, 2002). Kendall’s tau is a statistical test based on enumerating concordant (when both the x and y variables increase or decrease) and discordant (when x increases and y decreases or x decreases and y increases) pairs of x and y data (Kendall, 1938). Consequently, when stations have a substantial number of zero flows, causing ties in the pairs of x and y data, interpretation of the trend test can become tenuous at best. For hydrologic time-series data, Kendall’s tau is best suited for analysis of long-term datasets. Although it can be applied to short time series, Kendall’s tau may not provide information that is of practical importance, and care is needed to avoid misinterpreting results. Tests applied to short time series may (1) fail to detect a statistically significant trend even though a large increase or decrease in flow has been measured, or (2) detect a statistically significant trend even though the trend is of no practical importance (Oki, 2004). Thus, long-term streamgaging data are better suited for trend assessments. The USGS typically considers 30 years of streamflow record as a minimum requirement for assessing long-term trends (Lins, 2005). Nonetheless, results of the Kendall’s tau analysis are provided for all streamgages included in the study (tables 1 and 2 in Kolb and others, 2026). Additional trend analyses were completed for long-term streamgages and are discussed in later sections of this report.

Monotonic upward and downward trends were statistically assessed by using the Mann-Kendall test (Kendall, 1938; Mann, 1945) and the magnitude of trends was calculated by using the Theil-Sen estimator (Theil, 1950a, b; Sen, 1968). The Mann-Kendall test is a nonparametric test of trend based on the ranks of the observations. The Theil-Sen estimator is a robust, non-parametric method for simple linear regression and is calculated as the median of all possible pairwise slopes. The null hypothesis for the Mann-Kendall test was no monotonic trend (trend either upward or downward, without reversing direction). Statistically significant monotonic trends can be the result of a step change or another trend that may be best described as nonmonotonic. This analysis was limited to reporting the overall changes for the time periods tested.

In annual series data, short-term climatological variability could indicate serial correlation when assessed by using the Mann-Kendall test. For instance, the droughts of 1998 to 2002 and 2007 to 2008 in the southeastern United States spanned multiple CYs, setting record lows and likely causing the lowest flows each year (Weaver, 2015). By not accounting for persistence, such as a period of drought, the statistical significance of trends may be overstated (Cohn and Lins, 2005). Further, identification of a significant trend can be confounded by the presence of positive or negative autocorrelation in a time series. Thus, previous researchers have suggested statistical trend tests that modify the standard Mann-Kendall test to account for autocorrelated data (Hamed and Ramachandra Rao, 1998; Hamed, 2008). These modifications do not affect the power of the test to detect a trend and offer improved accuracy in significance levels (Hamed and Ramachandra Rao, 1998). The Type I error (that is, detecting a trend when none exists) is more prevalent due to the slow decay of the autocorrelation function when the time scale, the period of record, is greater than annual (Hamed, 2008). For this study, the shortest span analyzed was 30 years; thus, modified Mann-Kendall tests were used to account for autocorrelation.

Three dependence assumptions were tested: (1) independence (the standard Mann-Kendall test; Kendall, 1938; Mann, 1945), (2) short-term persistence (Hamed and Ramachandra Rao, 1998), and (3) long-term persistence (Hamed and Ramachandra Rao, 1998; Hamed, 2008). The three versions of the Mann-Kendall test all use the same test statistic, but the short-term persistence version inflates the variance computed by using the independence assumption by a factor related to the lag-1 autocorrelation coefficient, and the long-term persistence version inflates the variance based on the Hurst coefficient (Hurst, 1951). Data analysis was conducted in R version 4.4.0 (R Core Team, 2023). R scripts used to modify the Mann-Kendall test were obtained from the USGS New England Water Science Center. The scripts were originally written in 2014 by Benjamin Renard (IRSTEA, National Research Institute of Science and Technology for Environment and Agriculture, Lyon, France), for usage in USGS streamflow trend detection papers (Hodgkins and others, 2019; Dudley and others, 2020) and are available in a USGS data release (Dudley and others, 2018).

Graphical analysis of data was completed by using scatterplots and curve fitting. Temporal patterns in low-flow data were visualized with locally estimated scatterplot smoothing (LOESS) curves. Analogous to a moving average, the LOESS curve is a smoothing procedure for time-series data (Cleveland and Devlin, 1988). LOESS curves were fit to the data by using the “Exploration and Graphics for RivEr Trends” (EGRET) R package and the plotFlowTrend function (Hirsch and De Cicco, 2014; Hirsch and others, 2023). To aid in the visualization of long-term trends, the Theil-Sen estimator (also known as the Sen’s slope estimator or Kendall-Theil robust line) was used to fit patterns in low-flow data. The Theil-Sen estimator is a robust, nonparametric regression method for fitting a linear trend for data that may contain outliers or non-normal errors (Helsel and others, 2020). The slope is equal to the median of the slopes between all possible pairs of data. The Theil-Sen estimator was calculated with the “Median-Based Linear Models” R package by using the mblm function (Komsta, 2019). The method of computation for the statistical significance of the Theil-Sen estimator is identical to that of the Kendall’s τ coefficient (Helsel and others, 2020).

Two climatological influences on low flows are precipitation and air temperature. As such, trend analyses were completed for mean annual precipitation (CYs 1896–2021) and mean annual temperature (1895–2021) for Georgia, North Carolina, and South Carolina. Data for these analyses were obtained from the National Oceanic and Atmospheric Administration (NOAA) National Centers for Environmental Information website (NOAA, 2024a). These analyses covered 24 climate divisions (NOAA, 2024b, 2026, 9 climate divisions in Georgia, 8 climate divisions in North Carolina, and 7 climate divisions in South Carolina) and statewide aggregates for the 3 States (fig. 3). Trend analysis was completed by using the same methods and three dependence assumptions (independence, short-term persistence, and long-term persistence) applied to the annual minimum 7-day average flows. Graphical assessments included LOESS curves to visualize patterns in the data and the Theil-Sen robust line to visualize trends.

Examples of trends over time are shown in figure 4 for streamgages in Georgia, South Carolina, and North Carolina. Figure 4A shows no trend over time for USGS streamgage Oostanaula River at Resaca, Ga. (USGS site number 02387500; Alabama subregion, fig. 2), while figure 4B shows a downward trend over time at USGS streamgage North Pacolet River at Fingerville, S.C. (02154500; Edisto-Santee subregion), and figure 4C shows an upward trend over time at USGS streamgage Linville River near Nebo, N.C. (02138500; Edisto-Santee subregion).

For the 30-year climate period (CYs 1992–2021) for 78 streamgages, trend analysis in annual minimum 7-day average flows for the independence assumption (the standard Mann-Kendall test) indicated downward trends for 5 streamgages, an upward trend for 1 streamgage, and no statistically significant trends for 72 streamgages (table 2; table 3 in Kolb and others, 2026). Trend analysis using the short-term persistence assumption, indicated a downward trend for 1 streamgage, an upward trend for 1 streamgage, and no statistically significant trends for 76 streamgages. Trend analysis using the long-term persistence assumption indicated no statistically significant trends. Overall, this climate period is reflective of a largely stable pattern with minimal directional change.

For the 50-year climate period (CYs 1972–2021) trend analysis for 46 streamgages, there were downward trends in annual minimum 7-day average flows for 14, 10, and 1 streamgages for the independence, short-term persistence, and long-term persistence analyses, respectively; no statistically significant trends were indicated for the remaining streamgages (table 2; table 4 in Kolb and others, 2026). Assessing this trend data overall, the argument could be made that downward trends were a prominent feature of streamgage data during this period. However, during the 1960–70s, the southeastern United States was relatively wetter and cooler than the long-term normal (NOAA, 2024a). During 1998–2002, many areas in the southeastern United States experienced historic droughts (Weaver, 2005). As previously noted, in situations where a trend analysis begins and (or) ends in a relatively extreme condition, the trend test may indicate a statistically significant trend that may not actually be indicative of a longer term condition. This is likely the reason that the trend analysis considering long-term persistence for the period 1972–2021 indicates far fewer streamgages with statistically significant trends than the independence and short-term persistence analyses.

For the 70-year climate period (CYs 1952–2021) trend analysis for 27 streamgages, there were downward trends in annual minimum 7-day average flows for 7 and 6 streamgages for the independence and short-term persistence analyses, respectively, an upward trend in flows for 1 streamgage for the independence analysis, and no statistically significant trends for the remaining analyses (table 2; table 5 in Kolb and others, 2026). The lack of downward trends for the long-term persistence analysis as opposed to several downward trends for the independence and short-term persistence analyses, indicates that downward trends are not likely the result of longer term conditions—similar to the results from the 50-year climate period trend analysis.

For the 90-year climate period (CYs 1932–2021) trend analysis for six streamgages, there were downward trends in annual minimum 7-day average flows for two, two, and one streamgages for the independence, short-term persistence, and long-term persistence analyses, respectively; no statistically significant trends were indicated for the remaining analyses (table 2; table 6 in Kolb and others, 2026). Only a few streamgages were used in this analysis, and the majority indicated no statistically significant trend. All downward trends occurred within tests for two streamgages, indicating that minimum flows were decreasing at these sites.

Trend analysis indicated no statistically significant trends in mean annual precipitation for CYs 1896 to 2021 in either the statewide analysis or analysis by climate division for the independence, short-term persistence, or long-term persistence assumptions (table 3). Although not statistically significant, the Theil-Sen slope for the statewide analyses did indicate a slight total increase of 1.31, 1.74, and 1.74 inches of precipitation for Georgia, North Carolina, and South Carolina, respectively (fig. 5). With respect to the climate divisions, the Theil-Sen slope varied substantially. For example, the Central climate division in Georgia had a small total decrease of 0.14 inch, whereas the other climate divisions in Georgia had increases ranging from 0.13 inch in the Northeast to 3.67 inches in the Northwest (table 3).

Trend analysis for statewide mean annual air temperature for calendar years 1895 to 2021 that were done by using the dependence assumptions indicated upward trends for all three States (table 4; fig. 6). The independence trend analysis indicated upward trends for four climate divisions in Georgia, with total change from the Theil-Sen slope ranging from 0.81 to 1.14 °F; the remaining five divisions had no statistically significant trends. For North Carolina, seven climate divisions had statistically significant upward trends in air temperature, with total change ranging from 1.22 to 1.65 °F, whereas the Southern Mountains climate division had no statistically significant trend. All seven climate divisions in South Carolina had statistically significant upward trends in air temperature, with total change ranging from 0.83 to 1.20 °F. The long-term persistence analysis indicated that air temperature increases were not statistically significant.

Streams are impounded for a variety of reasons such as flood control, water supply, irrigation, and hydroelectric power generation (Ruddy and Hitt, 1990). The effect of the regulation from those various impoundments on downstream flows also varies widely (Feaster and Musser, 2023). For example, a water-supply reservoir may have little to no storage capacity for flood control and, consequently, not appreciably change the characteristics of downstream flood flows. Reservoirs where the main function is hydroelectric power generation or flood control will tend to decrease flood flows but may increase low flows (Graf, 2006). With respect to frequency analyses of regulated streams, a frequency analysis can be deemed reasonable if the period of record being analyzed has been determined to be a period when regulation patterns have been relatively stable and the statistical distribution used in the frequency analysis provides a reasonable fit to the data (Feaster and others, 2023). For regulated streamgages included in this report—for which low-flow frequency statistics are provided—graphical analysis of data, including scatterplots, LOESS curves, and single-mass curves, and trend analysis, as previously discussed, were used to assess the relative stability of regulation patterns, and low-flow frequency curves were reviewed to determine that the statistical distribution was reasonable for the analysis used here.

Determining a true natural condition in a stream or accurately accounting for all diversions in a basin is generally difficult. Diversions from natural flow can occur for many reasons (Ries, 1994; Feaster and Lee, 2017). Some diversions result from water-supply withdrawals, manufacturing processes, point-source discharges, and irrigation. In some cases, streamflow diversions may only affect flows for a short distance along the stream. For instance, water might be removed from a river, passed through a manufacturing plant for use in processing, cooling, or dilution of wastes, and then returned to the river. Under such conditions, consumptive losses from the diversion may be negligible. Subsequently, the effects of diversions on the streamflow regime of a river are variable and depend on the location of the diversion with respect to where streamflow is being monitored, the use (consumptive or not), and the return location of diverted water.

Water diverted from a stream or adjacent aquifer for municipal supplies often is returned to the same basin as effluent from individual septic systems or wastewater-treatment plants, which generally causes little loss of water to the basin; however, such diversions may affect the temporal pattern of streamflow (Ries, 1994). Diversions from one basin to another reduce streamflow in the donor basin and increase streamflow in the receiving basin. Diversions between subbasins of a larger basin may substantially affect streamflow in the subbasins, but if consumptive losses are negligible, streamflow in the larger basin may be nearly unaffected. These various diversion scenarios indicate that an accurate accounting of all diversions in a basin is generally problematic; therefore, most USGS low-flow studies, including this study, are based on the flow data as measured at the streamgage without adjustments for diversions.

Some of the long-term streamgages in the Coastal Plain Physiographic Province of Georgia (Georgia Coastal Plain; fig. 2) indicated a change in the pattern in annual minimum 7-day average flows around 1980, based on single-mass curve assessment of those minimum flows over time (see sidebar “Example of Single-Mass Curve Analysis”). Much of the decrease in annual minimum 7-day average flows likely resulted from increases in irrigation groundwater withdrawals that began in this region around 1980; although, determining all factors influencing the decrease in minimum flows was beyond the scope of this investigation. In the Georgia Coastal Plain, a substantial amount of water is used for agricultural irrigation (Painter, 2019), mostly from groundwater withdrawals (Henley, 2023; Hicks and others, 1987), and has contributed to long-term groundwater-level declines that have affected streamflows (Hicks and others, 1981, 1987; USGS, 2026). Williams and others (2017) documented large increases in irrigated acres in the Georgia Coastal Plain beginning between 1980 and 1984 and continuing through the end of their study, based on center pivot irrigation systems identified from Landsat images between 1976 and 2013. Based on this study, irrigated areas represented 4.1 percent of the Georgia Coastal Plain in 2013 and were concentrated in southwest Georgia.

For the 13 Georgia Coastal Plain streamgages for which change in flow was detected around 1980, the streamflow prior to 1980 was assumed to represent more natural conditions; therefore, streamflow frequency statistics from that period were included in regional regression analysis (Kolb and others, 2026, table 1). Streamflow frequency statistics also were calculated for these streamgages for the period after 1980 through CY 2021, but these data were not included in regression analysis (Kolb and others, 2026, table 2). These 13 streamgages are identified as having a flow condition of diversions, a remark indicating the partial period was excluded due to anthropogenic influences, and a period starting around CY 1980 in table 2 in Kolb and others (2026).

For streams with multiple streamgages, an assessment was made to determine potential redundancy of streamgages to be included in the regional regression analysis. Redundancy occurs when the drainage basins of two streamgages are nested, where one basin is inside another basin, and most or all streamflow records at the two streamgages represent concurrent periods of time (Gruber and Stedinger, 2008). For this investigation, a streamgage was considered redundant if it was on the same stream as another streamgage and the drainage area of one streamgage contained more than 50 percent of the drainage area of the second streamgage, unless there was an insignificant overlap in the period of record for the two streamgages.

Streamflow statistics can be estimated at ungaged sites by using multiple linear regression techniques that relate streamflow characteristics computed at gaged sites (such as the 7Q10 flow) to selected basin characteristics (hydrography, elevation, ecoregion, land use, soil, surficial geology, and climate) computed for the gaged drainage basins (table 5). Delineating basin boundaries at the USGS streamgage locations is the first step in generating potential basin characteristics for the regional regression analyses. Drainage-basin boundaries for this study were generated by using the USGS StreamStats application (Ries and others, 2017, 2024; USGS, 2019). Basin characteristics chosen for testing as potential explanatory variables were selected based on their potential theoretical relation to low flows, results of previous studies of low-flow regionalization, and the ability to quantify the basin characteristics by using a geographic information system (GIS). The use of GIS enables automation of the determination of basin characteristics and solution of the regional regression equations when using the USGS StreamStats application.

A regional regression analysis is an iterative process (Farmer and others, 2019; Feaster and others, 2020). The initial step involves computing streamflow statistics of interest along with potential basin characteristics (hydrography, elevation, ecoregion, land use, soil, surficial geology, and climate; table 5). Model development involves exploratory data analysis to get a general understanding of relations among the variables that are to be predicted, which can be referred to as the dependent or response variable (for example, the 7Q10 streamflow statistic), and certain basin characteristics, which can be referred to as the independent or explanatory variables (for example, drainage area). Often the estimation step begins with assessing the complete study area by testing all potential independent variables with a dependent variable of choice such as the 7Q10, which is referred to as an all-possible-subsets regression analysis. The results are then evaluated based on statistical significance of the independent variables, adherence to the assumptions of the regression techniques being applied, which are typically assessed based on the residuals computed from the difference in the observed and predicted dependent variable, and the geographical distribution of those residuals. Mapping the geographical distribution of the residuals provides information on potential subregions that might be warranted to improve the uncertainty in the predictions. Once a set of regional regression equations has been determined, the final step is to document the process with ample detail such that users of the equations have a general understanding of the proper application of the equations.

For an exploratory regression analysis, it is best to start with the largest reasonable region, which is often the complete study area (Farmer and others, 2019). The initial regression analysis for this investigation included the complete study area, and from there, several potential subregions were tested. The exploratory regression analysis was done by using ordinary least squares (OLS) regression techniques (SAS Institute, 2024). The general model for an OLS regression analysis is of the form:QT=a×Ab×Bc×Cd,(4)where

One of the assumptions of multiple linear regression is that the residuals are homoscedastic, meaning that they are equally dispersed throughout the range of the explanatory variables (Helsel and others, 2020). To obtain homoscedasticity, it is often necessary to transform the response variable and one or more of the explanatory variables. If the response and explanatory variables are logarithmically transformed, which is often the case with streamflow statistics, the regression model has the following form:log QT=log a+b(logA)+c(logB)+d(logC)+…,(5)where the variables are as previously defined in equation 4. Both logarithmic and arithmetic relations were used in this investigation because the logarithmic transformation of some variables did not improve the linear relation with Q_T.

At some of the streamgages included in this study, the low-flow frequency statistics were zero. When logarithmic transformation is used in a regression analyses, having response variables with a zero value is problematic because the logarithm of zero is undefined. In such cases where a relatively small percentage of the response variables is zero, left-censored regression, also referred to as Tobit regression (Tobin, 1958), can be used to overcome this issue. Helsel and Hirsch (2002) suggested that censored regression is appropriate for small to moderate amounts of censoring. Hirsch and others (1993) suggested censored regression is appropriate if censoring does not exceed 50 percent of observations.

Censored regression includes the uncensored and censored data and is similar to multiple linear regression, except regression coefficients are fit by maximum-likelihood estimation (MLE; Helsel and Hirsch, 2002; Eash and Barnes, 2012). MLE is comparable to a curve-matching process, in which a probability distribution is best matched to the observed data. MLE assumes that residuals are normally distributed around the regression line for the estimation of the slope and intercept and that the range of predicted values has constant variance. Cohn (1988) has shown that censored regression estimates are slightly biased, and an adjustment for first-order bias in these estimates is made by an adjusted maximum-likelihood estimation (AMLE) computation. An AMLE procedure implemented in the USGS-R/smwrQW package (Lorenz, 2014), which is available at https://rdrr.io/github/USGS-R/smwrQW/, was used to develop the left-censored regression equations in this study.

For the final regional regression equations developed in this study, weighted left-censored regression techniques were used, with weights based on the number of climate or water years of record (Lorenz, 2014; Ziegeweid and others, 2015; Gotvald, 2017). For datasets that do not contain censored values, weighted left-censored regression provides the same results as weighted least squares regression (Helsel and Hirsch, 2002). In censored regression for low-flow studies, the selected censoring level is typically a low streamflow value, such as 0.01, 0.05, or 0.1 cubic foot per second (ft³/s). For example, a censoring level of 0.1 ft³/s has been used in low-flow studies by Eash and Barnes (2012), Gotvald (2017), Feaster and others (2020), and Lukasz (2021). For this study, a censoring level of 0.05 ft³/s was used for consistency with the flow design criteria from the North Carolina Department of Environmental Quality, Division of Water Resources, for developing water-quality-based effluent limitations (North Carolina Department of Environment and Natural Resources, 2006).

Final selection of the independent variables to include in the regression models was based on several factors such as statistical significance, standard error, coefficient of determination, and ease of measurement of the explanatory variables. Correlation among the explanatory variables (multicollinearity) was assessed by using the variance inflation factor (VIF). If one or more VIF values exceed 5, the regression coefficients are likely poorly estimated due to multicollinearity (Montgomery and others, 2012). In such a case, one of the explanatory variables should be removed and the regressions reanalyzed to assess the remaining variables. All independent variables were considered statistically significant with a p-value of ≤0.05, and the VIF for all independent variables indicated no issues of multicollinearity among the variables.

For the OLS and left-censored regression analyses, multiple regression diagnostics were generated and used to identify possible problems with the streamgage data or basin characteristics. Along with reviews to ensure that the regression residuals were randomly distributed around zero and that they were reasonably distributed geographically, other regression diagnostics were reviewed to determine streamgages that had high leverage and (or) high influence (Eng and others, 2009). The leverage metric is used to measure how unusual the values of independent variables at one streamgage are compared to the values of the same variables at all other streamgages. The influence metric indicates whether the data at a streamgage had a high influence on the estimated regression metric values. A streamgage may have a high leverage metric indicating that its independent variables are substantially different from those at all other streamgages, but the same streamgage may not have a high influence on the regression metrics. Conversely, a streamgage with a high influence may not have a high leverage metric. Sometimes, measurement or transposing errors in reported values of some independent variables can produce high leverage or influence metrics. Streamgages with high influence or leverage were given additional review to determine if such errors had been made or if the streamgage should be excluded for other reasons.

For this study, regional regression equations were developed for 30 low-flow statistics and the mean annual flow. The 30 low-flow statistics were the annual 1Q10, 7Q2, 7Q10, 30Q2, and 30Q3, the W7Q10, and monthly (January–December) 1Q10 and 7Q10 statistics (table 6). The regression analyses included 604 streamgages from 7 States (table 7). For those 604 streamgages, the distribution of the systematic record lengths included in the regression analyses is shown on figure 10.

For low-flow frequency regression equations, the dominant independent variables were base 10 logarithm of drainage area (logDA), SVI, and mean annual precipitation (MeanAP). In 25 of 31 regression equations, percentage of impervious area (IA) was statistically significant, indicating that the regression equations are suitable for urban basins. The six equations for which IA was tested but was not statistically significant were Jan1Q10, May1Q10, Dec1Q10, Jan7Q10, May7Q10, and Dec7Q10. Because IA was tested but was not statistically significant, those equations also are considered applicable for use in urban basins.

Mean annual precipitation and SVI are regional variables in the regression equations. To account for additional regional differences, percentages of drainage basins in Level III and IV ecoregions also were tested as independent variables. All final regression equations include one or more independent variables that represent the percentage of basin in Level III and (or) Level IV ecoregions (fig. 1; EPA, 2013; Omernik and Griffith, 2014). When regression equations are applied in basins for which independent variables for the Level III or IV ecoregions are zero, those variables drop out, and the regression equation is just a function of the remaining variables. For example, if the Jan7Q10 equation is applied at an ungaged location that drains 100 percent from the Piedmont ecoregion, the percentage of basin draining from the Southwestern Appalachians, Sand Hills, and Southern Coastal Plain ecoregions is zero, and the equation then becomes a function of just logDA, SVI, and MeanAP.

Figure 11 provides an example of plots of the observed and predicted mean annual flow (fig. 11A), 1Q10 (fig. 11B), 7Q2 (fig. 11C), and 7Q10 (fig. 11D), along with the line of equality. The plots indicate a reasonable scatter distribution around the line of equality throughout the range of flows. Similar plots also were reviewed for all the other frequency statistics.

The accuracy (or uncertainty) in a regression model is evaluated based on the residuals (or error)—the differences between the predicted and observed values. Regression equations are statistical models that should be interpreted and applied within the limits of the data and understanding that results are best-fit predictions with an associated scatter or variance about the regression curve (Farmer and others, 2019; Feaster and others, 2023).

At-site low-flow frequency estimates at a USGS streamgage can be weighted with the regression prediction at the streamgage by using the weighting procedures outlined in USGS (2010) and England and others (2018). The weighting procedure for the low-flow frequency statistics is done by using the at-site variance from the LPIII analysis and the variance from the regression model as shown in equation 13. A weighted variance for the weighted low-flow prediction can be computed by using equation 14. Note that the weighted low-flow frequency prediction is computed by using base 10 logarithms and then transformed back to arithmetic units (eq. 15). To weight an at-site estimate that was not included in the regression analyses, replace the variance from the regression estimate with the average variance of prediction from table 6.logQws=VrslogQs+VslogQrsVs+Vrs,(13)whereQ_w(s)

is the weighted low-flow frequency estimate at a streamgage, in cubic feet per second;

Transformation of the low-flow frequency estimate back to arithmetic units, in cubic feet per second, is shown in equation 15:

Confidence intervals for the weighted estimate also can be computed. The upper and lower 95-percent confidence intervals (95%CI) on the weighted low-flow frequency estimate can be computed as95%CI=[10logQws−1.96Vws, 10logQws+1.96Vws,(16)where all variables are as previously defined.

Sauer (1974) presented a method to transpose a weighted frequency estimate from a streamgage to a nearby ungaged site on the same stream when the drainage area of the ungaged site is within plus or minus 50 percent of the drainage area at the gaged site. Many USGS flood-frequency reports have presented the method as a two-step process, with the first step being to transfer the weighted flow estimate at the streamgage to the ungaged location by using the following equation:Qu= Au/Agb×Qws,(17)where

Before simplifying, the ratio in equation 17 represents the ratio of the regression flow estimate at the ungaged and gaged locations when the regression equation is just a function of drainage area and when the two locations are in the same hydrologic region. As such, and before simplifying, equation 17 could be written as Q_u = (CA_u^b/CA_g^b) × Q_w(s), where C is the regression constant, and the other variables are as previously defined. Thus, in a case where the regression equation is a multivariable equation, such as the low-flow frequency equations from this report, the equation for Q_u would be as follows:Q_u = (Q_r(u)/Q_r(s)) × Q_w(s),(18)where Q_r(u) is the low-flow frequency estimate from the regression equation at the ungaged site and the other variables are as previously defined.

The final step in the procedure for transferring the weighted at-site estimate to an ungaged location is shown in equation 19:

The farther away the ungaged location is from the gaged location, equation 18 gives more weight to the regression prediction, Q_r(u). When the ungaged location is 0.5 or 1.5 times the drainage area of the gaged location, equation 19 gives full weight to Q_r(u). The two-step process can be done in a single step by combining equations 18 and 19, which results in equation 20:Qwu=2ΔAAs+1−2ΔAAsQwsQrsQru,(20)where

The low-flow frequency and mean annual flow regression equations developed during this study will be incorporated into the USGS StreamStats application (https://www.usgs.gov/streamstats; USGS, 2019) for Georgia, North Carolina, and South Carolina. USGS StreamStats is a web-based GIS application that provides a range of analytical tools for water-resource managers, planners, and engineers (Weaver and others, 2012; Ries and others, 2017; Feaster and others, 2018). The StreamStats application can be used to delineate drainage areas, generate basin characteristics, and compute estimates of streamflow statistics for user-selected sites through consistent and repeatable methods.